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Physics kinematics problem

  1. Feb 2, 2009 #1

    jgens

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    Gold Member

    1. The problem statement, all variables and given/known data
    You throw an object directly upward at the same time a person drops an object down to you from a height, H. The two objects pass at a height H/2. With what speed did you throw the object upward?


    2. Relevant equations
    Simple kinematics equations.


    3. The attempt at a solution
    I haven't done physics for a while so I'm not certain if I'm entirely off track on this one:

    I set up two equations for the motion of the balls (I'm allowing g = -10m/s/s); hence, I got h_a = (gt^2)/2 + H and h_b = (gt^2)/2 + vbi(t) where h_a is the height of the ball being dropped and h_b is the height of the ball being thrown (sorry if my notation is poor or non-standard). Since the balls are released simultaneously and pass at height H/2, I allow t1 to designate the amount of time required for the balls to reach H/2. By equating the two (h_a = h_b = H/2) I get (gt1^2)/2 + H = (gt1^2)/2 + vbi(t1), which solving for vbi produces vbi = H/t1. To solve for t1 I set up the equation H/2 = (gt1^2)/2 + H, and with some manipulations get t1^2 = -H/g and consequently t1 = sqrt(H/abs(g)). Using my value for t1 in my equation for vbi yields vbi = H(sqrt(abs(g)/H) = sqrt(Habs(g)).

    Sorry the work is so messy, I don't know how to use Latex.
     
  2. jcsd
  3. Feb 2, 2009 #2

    Delphi51

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    Homework Helper

    Looks good to me! Nicely done.
     
  4. Feb 2, 2009 #3

    jgens

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    Gold Member

    Thanks!
     
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